12.19 The authors of the paper “The Relationship of Field of Study to Current Smoking Status Among College Students” (College Student Journal [2009]: 744–754)

carried out a study to investigate if smoking rates were different for college students in different majors.

Each student in a large random sample of students at the University of Minnesota was classified according to field of study and whether or not they had smoked in the past 30 days. The data are given in the accompanying table.

Field of Study Smoked in the Last 30 Days Did Not Smoke in Last 30 Days 1. Undeclared 176 489 2. Art, design, performing arts 149 336 3. Humanities 197 454 4. Communication, languages, cultural studies 233 389 5. E ducation 56 170 6. Health sciences 227 717 7. Mathematics, engineering, sciences 245 924 8. Social science, human services 306 593 9. Individualized course of study 134 260

a. Is there evidence that field of study and smoking status are not independent? Use the Minitab output on the next page to test the relevant hypotheses using a 5 .01. (Hint: See Example 12.8.)

p1 is the proportion who usually eat three meals a day for males and p2 is the proportion who usually eat three meals a day for females. Minitab output from the two-sample z test is shown below.
Using a significance level of .05, does the twosample z test lead to the same conclusion as in Part (a)?
Test for Two Proportions Sample X N Sample p Male 26 48 0.541667 Female 37 91 0.406593 Difference 5 p (1) - p (2)
T est for difference 5 0 (vs not 5 0): Z 5 1.53 P-Value 5 0.127

d. How do the P-values from the tests in Parts (a)
and

(c) compare? Does this surprise you? Explain?